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Anyone For T - 2006 Maths Coursework.

Hello, I have Maths coursework to finish v.soon here is the question :


"Anyone for T

A 10 by 10 grid is numbered consecutively from 1 to 100



The grid has the letter T placed upon it, as shown on the diagram.
This T has a horizontal bar length of 3 and a vertical bar length of 2.

The number at the bottom of the vertical bar is squared and the numbers at each end of the horizontal bar are multiplied. One answer is then subtracted from the other. This result is called the T value.

This is the working for T13
34² = 1156
13 x 15 = 195
So T13 is 1156 -195 = 961

1 Investigate T values in this way
2 Extend your investigation, making clear the rules and methods that you use"


So far I have got the equation:

20n+121 = 5 x 5 grid

40n+441 = 10 x 10 grid and so on

I then worked out another rule which you wouldn't need to draw out the grid and it wouldn't matter what the size of the grid was, the equation is :
4wt + (2w+1)^2

t = nth term i.e. the top left number in the t ie 1 2 3
11 12 13
21 22 23
t = 1 on this pattern
w= width of grid i.e. in 10 x 10 grid w would equal 10

I now need to extend "t" to give me a 3 letter in the equation any help please.... I looked on coursework.info but no courseworks on this and I spend 10 pounds too :frown:..

Anyone done this can give me the equation answer with 3 letters please...

also my msn is [email protected]

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Reply 1
Nope. This is coursework you're talking about, so giving away answers would defeat the point. If you have any general questions regarding the underlying mathematics (e.g. interpreting the question, working with sequences and series, algebraic manipulation etc) then a lot of people will be more than happy to help :smile:.
Reply 2
.... There stopping coursework man...

www.coursework.info which is connected to this site give answers away....

I don't understand I don't want to copy someone else coursework I just need the answer... Someone in my class found it out of there dad as he teachers GCSE too but he won't tell me.
Reply 3
But w/e please Anything just help me I already have a "b" grade with what I have, I just want an "A" and to do this I need a 3rd letter in my equation.

Its not as if I am asking someone can I copy and there coursework and paste it into word man..
Reply 4
Is this about the T-Total Number based Coursework?? Is it where you have to do the 9 by 9 grid and other size grids to find the nth term and n's. And after that you use G by G grid to rotate, reflect and enlarge the T to find the nth term?

As im doing that as well. what tier (founda,interm,higher) are you in??
Reply 5
Doing higher...

Basically I have found an equation which works for any size grid all you need to know if the nth term and the grid you would do it on and you don't need to draw out the grid to work out the value..

Now I need to extend T downwards... and have the same equation as before but with an extra letter to represent the height of t. And then even with high t,different grid and different nth term you could still work t out without drawing t t on a grid.

then if you want A* coursework you need an equation that would work all the above but then if you rotated t lets say 90 degrees...
Reply 6
Any help please I have to finish this by monday :O
Reply 7
I did this coursework in year 11, eesh it was a pain, i ended up doing about 30 pages or something silly.

So are you looking to extend the t by a stretch or just translate it down the grid and find a formula for that?
Reply 8
add one down... i.e. instead it being 3 down it will be 4 down... I will need to get a letter i.e. "H" and put that in my equation... so if you extend t down extra by lets say 5 boxes .. you will put that in the equation...and sitll be able to work out answer with just the equation and no need to draw the grid.
Reply 9
Think about the horizontal numbers, i.e call the first one n then along the top row you would have n+1,n+2 etc
find a formula in terms of n for the top left number times the top right.

Then look at the bottom number when you have a normal t, can you find a fomula for that in terms of n? this will vary on grid sizes obviously, but use a 9x9 to get the hang of it.

Now if you take one from the other, it will give you a formula for t in terms of n which is the top left hand number.

Try this again with different grid sizes to get the rule and call that w or what ever, now put that into your formula to find t.

Then extend the t downwards, again find the relationship between the first number in the t and the very bottom. Now find an equation for t like you did before, what is different about the two equations? Is there a number in one that is different to another? find what has happened to the first equation to get the second, then generalise.

Sorry if that isn't how you approached the coursework, i seem to remember doing mine that way, then for a* it moves onto rotation. good luck!
Reply 10
I already have "4wt + (2w+1)^2" which means that on anysize grid moving the t anywhere on that grid i can work out from this formula... now if i extend t i need to add to this formula.
Reply 11
Well if you extend the t by one downwards.. then the number you sqaure by is 5 more greater on a 5x5 grid and 10 greater on a 10 x 10 grid... i.e... if i extend t by 1 on a 4 by 4 grid the number i square by should be +4 more greater instead of being lets say 14^2 it would be 18^ but still dont get how to link this into an equation...
Reply 12
swatjosh
Well if you extend the t by one downwards.. then the number you sqaure by is 5 more greater on a 5x5 grid and 10 greater on a 10 x 10 grid... i.e... if i extend t by 1 on a 4 by 4 grid the number i square by should be +4 more greater instead of being lets say 14^2 it would be 18^ but still dont get how to link this into an equation...



Well if you let your grid size = g*g

Have you found a formula for the number you square by?

Try find it in terms of the top left hand number, it's quite easy to generalise for any grid once you find it for a 9*9 then a 10*10, you'll see a pattern.

Get your T to equal (number you square by +g)^2 - [(the first number)(3rd number)]

n = 1st number on any grid size
n+2 = 3rd number on any grid size

square brackets = n*(n+2)

and see what happens
Reply 13
Huh? Don't understand you.... I already have a forumla done for The "T" and changing the grid size on which the T lies... The formula is "4wt + (2w+1)^2"

I believe the extension of t had something to do with +1) part in the equation but I don't know what...
Reply 14
swatjosh
Huh? Don't understand you.... I already have a forumla done for The "T" and changing the grid size on which the T lies... The formula is "4wt + (2w+1)^2"

I believe the extension of t had something to do with +1) part in the equation but I don't know what...


Well look at how you proved your equation for T, if you add 1 w onto the bottom number that you square for every extra square you go down then it should just be a matter of adding (w*y) where y = [the number of extra squares added] to the very bottom number and working through the algebra again like you did first time.
Reply 15
So :

I have worked out B + (W x H )

B = Bottom Number which would normally be sqaured

W = Width of grid i.e 10 x 10 grid the W = 10 or 5 x5 the W = 5

H = Hight Adjustment of grid i.e. instead of being 3 down its 4 down so H = 1

is this right ? am I going along the right lines... I don't think I need the B+ bit.
Try something flash like a grid full of triangular numbers instead of consecutive integers :smile:
Reply 17
Huh ???? That complicated... I need something that will work for a normal grid at different sizes an d a bigger t ... that will gurantee be a A if i explain it well.. and an A* if i can rotate with an equation.
Reply 18
swatjosh
So :

I have worked out B + (W x H )

B = Bottom Number which would normally be sqaured

W = Width of grid i.e 10 x 10 grid the W = 10 or 5 x5 the W = 5

H = Hight Adjustment of grid i.e. instead of being 3 down its 4 down so H = 1

is this right ? am I going along the right lines... I don't think I need the B+ bit.


zrancis is this right ? I still have to rotate "T" :O ???
Reply 19
Anyone ?